---
tag: AQDX1ECXKJ
kind: concept
name: Algebraic connectivity
aliases: [algebraic-connectivity-of-a-graph, fiedler-vector, fiedler-value]
sources:
  - wikipedia: en:3396069@r1348553826
    locator: Algebraic connectivity
    note: adopted
    mention: wikipedia://en/3396069
    sections: [Summary]
same_as:
  wikidata: Q4723998
  wikipedia: Algebraic connectivity
inventory: [5FFPB0QTKD]
---

## Summary

The **algebraic connectivity** (also known as **Fiedler value** or **Fiedler eigenvalue** after Miroslav Fiedler) of a [[graph|00C0BR7D7H]] *$G$* is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of *$G$*. This eigenvalue is greater than 0 if and only if *$G$* is a connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of connected components in the graph. The magnitude of this value reflects how well connected the overall graph is. It has been used in analyzing the robustness and synchronizability of networks.